I'll add a thought to the good answers here that it sounds as though you are using your characters to advance a plot point. While we all do this, allowing your characters to behave naturally with one another without any demands upon them can be an interesting exercise.
How would your characters interact in this scene if there was no need for them to expose the information you're trying to get across? Might be worthwhile to write that, and see what it looks like.
Also, for what it's worth, successful writers use 'tell' all the time. The advice to "show, not tell," is arguably analogous to someone saying a happy song should always be played in a major key; no minor chords allowed. Because major chords feel better, happier, and create the effect in the audience that you're going for.
Well, it's an interesting idea (...maybe...) but hardly an absolute. A musician learns to hear what a song needs, and likewise there's an ear for reading that a writer should try to develop. It's easier to hear the wrong notes in someone else's writing, but we all eventually learn to hear them in our own as well.
A story that is all tell would be tedious to read. that's probably the basis of the advice. And many writers start learning with telling. But every published novel on the market has some tell in it. Three weeks later... is telling. His hair was perceptibly longer, almost a half inch longer than the last time she had seen him... is, technically, showing. And a stupid way to say that three weeks had passed, if the point is to give a quick reference to the passage of time.
Here's an easy device you might try: Move some of the 'dialog exposition' into thought, and leave some in dialog.
How could I tell her that Jackie had killed her ex? That the affair between them had spiraled into a toxic nightmare so deep the entire town reverberated from it?
"I think it was a local. Single bullet to the head."
What that does is place exposition into an emotional context. It is most certainly telling the reader who killed 'her ex' (Jackie did), and why she had done so (some sort of affair gone bad) but it's doing it by wrapping the information into an emotional dilemma for the viewpoint character--and since the viewpoint character is withholding some information from the other character (but not from the reader) there's another layer of complexity. It doesn't feel like telling. And, some info is given in dialog (bullet to the head.) So that feels like verbal movement, not an info dump, if you take my meaning.
And, as a bonus, with this particular device, we come to know more than the character receiving the information, too, which is also sometimes useful in storytelling.
Answer: Telling is fine when appropriate, and there are ways to impart information beyond info-dump and dialog--such as immersing into a deeper viewpoint, so that the reader can 'know' the information from the experience of the viewpoint character.
(Using dialog as a crutch to 'avoid telling' is an early tool we acquire, and a good one, but too easily abused which it sounds like you may have done.)